Question

ab and cd intersect in the figure. use the figure to identify each pair of angles as complementary or supplementary.
complementary
supplementary
:: ∠1 and ∠2
:: ∠4 and ∠5
:: ∠1 and ∠5

Explanation:

Step1: Recall angle definitions

Complementary angles sum to \(90^\circ\), supplementary sum to \(180^\circ\). From the figure, \( \angle 3 = 90^\circ \) (right angle), so \( \angle 4 + \angle 5 = 90^\circ \) (complementary). \( \angle 1 + \angle 2 = 180^\circ \) (supplementary, linear pair), \( \angle 1 + \angle 5 \): since \( \angle 2 = \angle 5 \) (vertical angles), and \( \angle 1 + \angle 2 = 180^\circ \), so \( \angle 1 + \angle 5 = 180^\circ \) (supplementary).

Step2: Classify each pair

• \( \angle 1 \) and \( \angle 2 \): Linear pair, sum to \( 180^\circ \) → Supplementary.
• \( \angle 4 \) and \( \angle 5 \): Sum to \( 90^\circ \) (since \( \angle 3 = 90^\circ \), and \( \angle 4 + \angle 5 + \angle 3 = 180^\circ \)? Wait, no: \( AB \) is straight, \( E \) is perpendicular, so \( \angle 3 + \angle 4 + \angle 5 = 180^\circ \)? Wait, no, \( \angle 3 = 90^\circ \), so \( \angle 4 + \angle 5 = 90^\circ \) (complementary).
• \( \angle 1 \) and \( \angle 5 \): Vertical angles? No, \( \angle 1 \) and \( \angle 2 \) are vertical? Wait, \( AB \) and \( CD \) intersect, so \( \angle 1 = \angle 2 \) (vertical angles)? No, wait, \( AB \) is a straight line, \( CD \) intersects it, so \( \angle 1 + \angle 5 + \angle 4 + \angle 3 = 180^\circ \)? Wait, maybe better: \( \angle 1 \) and \( \angle 5 \): since \( \angle 1 + \angle 2 = 180^\circ \), and \( \angle 2 = \angle 5 \) (vertical angles), so \( \angle 1 + \angle 5 = 180^\circ \) (supplementary).

Answer:

• Complementary: \( \angle 4 \) and \( \angle 5 \)
• Supplementary: \( \angle 1 \) and \( \angle 2 \), \( \angle 1 \) and \( \angle 5 \)

(If the task is to drag each pair to the correct box:
Complementary box: \( \angle 4 \) and \( \angle 5 \)
Supplementary box: \( \angle 1 \) and \( \angle 2 \), \( \angle 1 \) and \( \angle 5 \))